Symmetry energy from the nuclear collective motion: constraints from dipole, quadrupole, monopole and spin-dipole resonances

The experimental and theoretical studies of Giant Resonances, or more generally of the nuclear collective vibrations, are a well established domain in which sophisticated techniques have been introduced and firm conclusions reached after an effort of several decades. From it, information on the nuclear equation of state can be extracted, albeit not far from usual nuclear densities. In this contribution, which complements other contributions appearing in the current volume, we survey some of the constraints that have been extracted recently concerning the parameters of the nuclear symmetry energy. Isovector modes, in which neutrons and protons are in opposite phase, are a natural source of information and we illustrate the values of symmetry energy around saturation deduced from isovector dipole and isovector quadrupole states. The isotopic dependence of the isoscalar monopole energy has also been suggested to provide a connection to the symmetry energy: relevant theoretical arguments and experimental results are thoroughly discussed. Finally, we consider the case of the charge-exchange spin-dipole excitations in which the sum rule associated with the total strength gives in principle access to the neutron skin and thus, indirectly, to the symmetry energy.Comment: Updated version, with small corrections based on comments/suggestions from the referee. 12 pages, 9 figures; submitted to EPJA "Special Issue on Symmetry Energy

Hygrothermal effects on mechanical behavior of graphite/epoxy laminates beyond initial failure

An investigation was conducted to determine the critical load levels and associated cracking beyond which a multidirectional laminate can be considered as structurally failed. Graphite/epoxy laminates were loaded to different strain levels up to ultimate failure. Transverse matrix cracking was monitored by acoustic and optical methods. Residual stiffness and strength that were parallel and perpendicular to the cracks were determined and related to the environmental/loading history. Results indicate that cracking density in the transverse layers has no major effect on laminate residual properties as long as the angle ply layers retain their structural integrity. Exposure to hot water revealed that cracking had only a small effect on absorption and reduced swelling when these specimens were compared with uncracked specimens. Cracked, moist specimens showed a moderate reduction in strength when compared with their uncracked counterparts. Within the range of environmental/loading conditions of the present study, it is concluded that the transverse cracking process is not crucial in its effect on the structural performance of multidirectional composite laminates

Effect of pairing correlations on incompressibility and symmetry energy in nuclear matter and finite nuclei

The role of superfluidity in the incompressibility and in the symmetry energy is studied in nuclear matter and finite nuclei. Several pairing interactions are used: surface, mixed and isovector dependent. Pairing has a small effect on the nuclear matter incompressibility at saturation density, but the effects are significant at lower densities. The pairing effect on the centroid energy of the isoscalar Giant Monopole Resonance (GMR) is also evaluated for Pb and Sn isotopes by using a microscopic constrained-HFB approach, and found to change at most by 10% the nucleus incompressibility $K_A$. It is shown by using the Local Density Approximation (LDA) that most of the pairing effect on the GMR centroid come from the low-density nuclear surface.Comment: 9 pages, 6 figure

Knuthian Drawings of Series-Parallel Flowcharts

Inspired by a classic paper by Knuth, we revisit the problem of drawing flowcharts of loop-free algorithms, that is, degree-three series-parallel digraphs. Our drawing algorithms show that it is possible to produce Knuthian drawings of degree-three series-parallel digraphs with good aspect ratios and small numbers of edge bends.Comment: Full versio

Quantum nucleation in ferromagnets with tetragonal and hexagonal symmetries

The phenomenon of quantum nucleation is studied in a ferromagnet in the presence of a magnetic field at an arbitrary angle. We consider the magnetocrystalline anisotropy with tetragonal symmetry and that with hexagonal symmetry, respectively. By applying the instanton method in the spin-coherent-state path-integral representation, we calculate the dependence of the rate of quantum nucleation and the crossover temperature on the orientation and strength of the field for a thin film and for a bulk solid. Our results show that the rate of quantum nucleation and the crossover temperature depend on the orientation of the external magnetic field distinctly, which provides a possible experimental test for quantum nucleation in nanometer-scale ferromagnets.Comment: 19 pages and 3 figures, Final version and accepted by Phys. Rev. B (Feb. B1 2001

Quantum Nucleation in a Ferromagnetic Film Placed in a Magnetic Field at an Arbitrary Angle

We study the quantum nucleation in a thin ferromagnetic film placed in a magnetic field at an arbitrary angle. The dependence of the quantum nucleation and the temperature of the crossover from thermal to quantum regime on the direction and the strength of the applied field are presented. It is found that the maximal value of the rate and that of the crossover temperature are obtained at a some angle with the magnetic field, not in the direction of the applied field opposite to the initial easy axis.Comment: 15 pages, RevTex, 3 PostScript figures. To appear in Phys. Rev.

Magnetic Field Dependence of Macroscopic Quantum Tunneling and Coherence of Ferromagnetic Particle

We calculate the quantum tunneling rate of a ferromagnetic particle of $\sim 100 \AA$ diameter in a magnetic field of arbitrary angle. We consider the magnetocrystalline anisotropy with the biaxial symmetry and that with the tetragonal symmetry. Using the spin-coherent-state path integral, we obtain approximate analytic formulas of the tunneling rates in the small $\epsilon (=1- H/H_c)$-limit for the magnetic field normal to the easy axis ($\theta_H = \pi/2$), for the field opposite to the initial easy axis ($\theta_H = \pi$), and for the field at an angle between these two orientations ($\pi/2 << \theta_H << \pi$). In addition, we obtain numerically the tunneling rates for the biaxial symmetry in the full range of the angle $\theta_H$ of the magnetic field ($\pi/2 < \theta_H \leq \pi$), for the values of \epsilon =0.01 and 0.001.Comment: 25 pages of text (RevTex) and 4 figures (PostScript files), to be published in Phys. Rev.

Quantum phase interference and spin parity in Mn12 single-molecule magnets

Magnetization measurements of Mn12 molecular nanomagnets with spin ground states of S = 10 and S = 19/2 showresonance tunneling at avoided energy level crossings. The observed oscillations of the tunnel probability as a function of the magnetic field applied along the hard anisotropy axis are due to topological quantum phase interference of two tunnel paths of opposite windings. Spin-parity dependent tunneling is established by comparing the quantum phase interference of integer and half-integer spin systems.Comment: 5 pages, 5 figure

Decoherence in Ion Trap Quantum Computers

The {\it intrinsic} decoherence from vibrational coupling of the ions in the Cirac-Zoller quantum computer [Phys. Rev. Lett. {\bf 74}, 4091 (1995)] is considered. Starting from a state in which the vibrational modes are at a temperature $T$, and each ion is in a superposition of an excited and a ground state, an adiabatic approximation is used to find the inclusive probability $P(t)$ for the ions to evolve as they would without the vibrations, and for the vibrational modes to evolve into any final state. An analytic form is found for $P(t)$ at $T=0$, and the decoherence time is found for all $T$. The decoherence is found to be quite small, even for 1000 ions.Comment: 11 pages, no figures, uses revte

Identification of Non-unitary triplet pairing in a heavy Fermion superconductor UPt_3

A NMR experiment recently done by Tou et al. on a heavy Fermion superconductor UPt$_3$ is interpreted in terms of a non-unitary spin-triplet pairing state which we have been advocating. The proposed state successfully explains various aspects of the seemingly complicated Knight shift behaviors probed for major orientations, including a remarkable d-vector rotation under weak fields. This entitles UPt$_3$ as the first example that a charged many body system forms a spin-triplet odd-par ity pairing at low temperatures and demonstrates unambiguously that the putative spin-orbit coupling in UPt$_3$ is weak.Comment: 4 pages, 2 eps figures, to be published in J. Phys. Soc. Jpn. 67 (1998) No.